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PCAT Quantitative Reasoning – Logarithms and Exponents

  • by Sam
  • Apr 19, 2018
  • PCAT Question of the Day

Log83 is closest in value to which of the following?

A. 3.5
B. 4
C. 4.5
D. 5

Click for Explanation

C is correct. First, let’s expand 83 and express this value in terms of 4:

log83 = log4(8 × 8 × 8) = log4(4 × 2 × 4 × 2 × 4 × 2) = log4(43 × 23) = log4(44 × 2)

We know the relationship between logarithmic and exponential expressions to be logab = c and ac = b, so let’s rewrite this expression as such:

4x = 44 × 2

Therefore, we know that our answer must be greater than x = 4 (44 = 256) but less than x = 5 (45 = 1024). Answer choice C is correct: 44.5 = 83 = 512.

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